Amy drove on the highways at 70 miles/hour to pick up fruits from her grandma’s garden in the morning. She stayed there for two hours. When coming back in the afternoon, she drove on the local roads at 40 miles per hour to avoid traffic. She spent a total of 8 hours for this trip, and drove
a total 300 miles. How many miles did she drive each way?

Let the distance Amy drove each way be denoted as \( d \) miles.

- On the way to her grandma's house, Amy drove on the highways at a speed of 70 miles per hour.
- On the way back, she drove on local roads at a speed of 40 miles per hour.
- She spent a total of 8 hours for the entire trip, and the total distance driven was 300 miles.

### Step 1: Setting up the distance equation
The total distance driven is the sum of the distances to and from her grandma’s house:
\[
d + d = 300
\]
\[
2d = 300
\]
\[
d = 150 \, \text{miles}
\]
So, the distance each way is 150 miles.

### Step 2: Setting up the time equation
The total time spent driving is the time it took to drive to her grandma's house, plus the time it took to drive back, plus the 2 hours she spent at her grandma's house. This total time is given as 8 hours.

The time taken to drive to her grandma’s house is:
\[
t_1 = \frac{d}{70} = \frac{150}{70} = \frac{15}{7} \approx 2.14 \, \text{hours}
\]

The time taken to drive back is:
\[
t_2 = \frac{d}{40} = \frac{150}{40} = 3.75 \, \text{hours}
\]

Now, the total time spent is:
\[
t_1 + t_2 + 2 = 8
\]
Substituting \( t_1 \) and \( t_2 \):
\[
\frac{15}{7} + 3.75 + 2 = 8
\]

### Step 3: Verifying the equation
First, convert 3.75 into a fraction:
\[
3.75 = \frac{15}{4}
\]

Now, solve the equation:
\[
\frac{15}{7} + \frac{15}{4} + 2 = 8
\]

Find a common denominator for the fractions:
\[
\text{LCD of 7 and 4 is 28}, \quad \frac{15}{7} = \frac{60}{28}, \quad \frac{15}{4} = \frac{105}{28}
\]

So the equation becomes:
\[
\frac{60}{28} + \frac{105}{28} + 2 = 8
\]
\[
\frac{165}{28} + 2 = 8
\]
\[
\frac{165}{28} = 6
\]
\[
6 + 2 = 8
\]

This confirms that the solution is correct.

### Final Answer:
Amy drove **150 miles each way**.

---

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would the time change if Amy had driven on the highway both ways?
2. What would the total time be if Amy had driven back at 60 miles per hour instead of 40?
3. How much time would she have saved if she avoided traffic and drove 70 miles per hour on the way back?
4. If the total time spent was 10 hours instead of 8, what would the distance each way be?
5. How many hours would Amy have spent driving if the total distance was 350 miles?

**Tip:** Always break down complex problems into smaller steps to simplify the solution process.

Amy drove on the highways at 70 miles/hour to pick up fruits from her grandma’s garden in the morning. She stayed there for two hours. When coming back in the afternoon, she drove on the local roads at 40 miles per hour to avoid traffic. She spent a total of 8 hours for this trip, and drove a total of 300 miles. How many miles did she drive each way?

This problem involves determining how many miles Amy drove each way, using algebraic concepts and distance-speed-time relationships. Amy drove 70 mph on highways and 40 mph on local roads, with a total distance of 300 miles and 8 hours for the trip. Suitable for students in Grades 7-10.

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